a)Ta có:A=3+32+33+...+318
=(3+32)+(33+34)+...+(317+318)
=3(1+3)+33(1+3)+...+317(1+3)
=3.4+33.4+...+317.4
Vì 4\(⋮\)4 nên 3.4+33.4+...+317.4\(⋮\)4
hay A\(⋮\)4
Ta có:A=3+32+33+...+318
=(3+32+33)+(34+35+36)+...+(316+317+318)
=3(1+3+32)+34(1+3+32)+...+316(1+3+32)
=3.13+34.13+...+316.13
Vì 13\(⋮\)13 nên 3.13+34.13+...+316.13\(⋮\)13
hay A\(⋮\)13
Vậy A chia hết cho 4, 13.
A=3+32+33+...+318
A=(3+32)+(33+34)+...+(317+318)
A=3(1+3)+33(1+3)+...+317(1+3)
A=3x4+33x4+...+317x4
A=4x(1+33+...+317) chia hết cho 4
a) A = 3 + 32 + 33 + ... + 318 Chia hết cho 4
= ( 3 + 32 ) + ( 33 + 34 ) + ... + ( 317 + 318 )
= 12 . 1 + 32 . ( 3 + 32 ) + ... + 316 . ( 3 + 32 )
= 1 . 12 + 32 . 12 + ... + 316 . 12
= 12 . ( 1 + 32 + ... + 316 )
= 4 . 3 . ( 1 + 32 + ... + 316 ) Chia hết cho 4
A = 3 + 32 + 33 + ... + 318 Chia hết cho 13
= ( 3 + 32 + 33 ) + ( 34 + 35 + 36 ) + ... + ( 316 + 317 + 318 )
= 1 . 39 + 33 . ( 3 + 32 + 33 ) + ... + 315 . ( 3 + 32 + 33 )
= 1 . 39 + 33 . 39 + ... + 315 .
= 39 . ( 1 + 33 + ... + 315 )
= 3 . 13 . ( 1 + 33 + ... + 315 ) Chia hết cho 13
b) A = 3 + 32 + ... + 318 Chia hết cho 364
= ( 3 + 32 + 33 + 34 + 35 + 36 ) + ( 37 + 38 + 39 + 310 + 311 + 312 ) + ( 313 + 314 + 315 + 316 + 317 + 318 )
= 1 . 1092 + 36 . ( 3 + 32 + 33 + 34 + 35 + 36 ) + 312 . ( 3 + 32 + 33 + 34 + 35 + 36 )
= 1 . 1092 + 36 . 1092 + 312 . 1092
= 1092 . ( 1 + 36 + 312 )
= 364 . 3 . ( 1 + 36 + 312 ) Chia hết cho 364
k mình nha
a) Ta có : A = (3 + 32 + 33) + (34 + 35 + 36) + ... + (316 + 317 + 318)
= 3(30 + 31 + 32) + 34(30 + 31 + 32) + ... + 316(30 + 31 + 32)
= 13(3 + 34 + ... + 316) \(⋮\)13 (đpcm).
A = (3 + 32) + (33 + 34 + 35 + 36) + (37 + 38 + 39 + 310) + ... + (315 + 316 + 317 + 318)
= 12 + 33(30 + 31 + 32 + 33) + 37(30 + 31 + 32 + 33) + ... + 315(30 + 31 + 32 + 33)
= 12 + 40(33 + 37 + ... + 315) \(⋮\)4 (đpcm)
b) Ta có : A = (3 + 32 + 33 + 34 + 35 + 36) + (37 + 38 + 39 + 310 + 311 + 312) + (313 + 314 + 315 + 316 + 317 + 318)
= 3(30 + 31 + 32 + 33 + 34 + 35) + 37(30 + 31 + 32 + 33 + 34 + 35) + 313(30 + 31 + 32 + 33 + 34 + 35)
= 364(3 + 37 + 313) \(⋮\)364 (đpcm).
